Costs and Outputs

Remembering Prof. Alchian's Insights

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At Economic Forces, our tagline is “Pondering price theory, past and present.” Obnoxious alliteration aside, we chose that because we think the past is also important to our understanding of price theory today. Economic history and the history of economic thought can teach us a lot about price theory.

For this week’s newsletter, I want to dig into a famous paper by Armen Alchian titled “Costs and Outputs,” both to remind myself of the insights and to let all y’all know. From my understanding, the paper grew out of confusion around the measurement of costs for weapons systems. Alchian wrote the paper for the RAND Corporation to help clarify for the military what they were actually measuring. As with any good price theory, the point of the theory is to better understand real-world problems.

Alchian’s paper emphasizes three aspects of costs that are ignored in most discussions of cost curves.

  1. The distinction between rate and quantity of output

  2. The use of capital value concepts of cost

  3. The use of calendar time for output

Let’s dig into these three points.

Rate vs. Quantity of Output

If people know Alchian’s paper, it’s for the first idea. As Jack Hirshleifer explained in a follow-up paper that you should also read, “The key idea [in Alchian} is that cost can be regarded as a function of the quantity of "output" in two different dimensions: rate of output, and scheduled volume of output.” This idea is really important and clarifies some confusion around cost-curves.

When we draw supply and demand, or just the cost curves underlying supply, we put the price (P) on the y-axis and the quantity (Q) on the x-axis. We (myself included) are often sloppy with the exact units we are considering and that leads to some confusion.

For example, we usually draw our cost curve, the marginal cost at least, as upward sloping. As quantity increases, cost increases. But when we look out at the world, higher quantities seem to be associated with lower costs. What gives?

Alchian gives us a partial reconciliation of this problem. The quantity we are graphing holds the time of production fixed. The “cost” should be thought of as a rate, quantity per unit time, instead of simply a quantity. If a factory needs to increase the quantity produced on a particular day, then it is more reasonable that costs increase with higher quantities per day. If we imagine our beloved widget factory and your shift leader is standing over your shoulder yelling more, you can produce more. But it gets harder to produce more widgets. In other words, production gets more costly.

While the rate/quantity distinction is important, it has tended to overshadow the two other ideas of Alchian’s paper. That’s unfortunate.

Capital Value of Costs

What really makes Alchian’s approach unique, and gives rise to the other insights, is that that he makes clear that costs should be defined as the “change in equity caused by the performance of some specified operation, where, for simplicity of exposition, the attendant change in income is not included in the computation of the change in equity.”

In other words, take any hypothetical action. Ignoring the income generated, go to the balance sheet and account for any relevant costs. Start with a present value of assets is currently $100 and you see that at the end of the action, which happens a year later, the value of assets will be $80. In present value terms (at 6%), the firm will be worth $75.47. Therefore the cost of that action is, in the relevant present value (equity) terms, is $24.53.

What surprised me when rereading this paper (based on Josh’s recent recommendation, thanks Josh!) is that Alchian defines cost as a stock variable(!), while everyone else takes Alchian to be emphasizing cost as a rate or flow variable.

Alchian argues that the use of capital values as the measure of costs helps us avoid misleading statements like “We are going to operate at a loss in the near future but operations will be profitable later.” That’s not wrong, and I say when teaching cost curves, but it is a bit misleading. Who would purposefully lose money? We have our stories but they are misleading.

Instead, people mean cash flows will be negative for some time, which isn’t the same as profits. We certainly have no serious theory of why a firm would generally maximize cash flow. We have a theory of why a firm would maximize equity.

Tieing to Alchian’s evolutionary theory of firm survival, firms can survive negative cash flows. Zero, or negative, equity is what ultimately filters out firms from the market.

If we take this idea seriously, we are left with a different paradigm on costs than most economists use. Capital theory, firm ownership, and salvage value become much more central than Chicago types would have you believe.

Calendar Time Output

The final distinction for Alchian has to do with time. The standard approach to cost curves, going back to Jacob Viner in 1931, makes a distinction between the “short-run” and the “long-run.” In the short-run, some inputs are fixed and cannot be varied. For example, a factory that uses workers and machines may not be able to install a new machine today but it can choose how many workers to put on the schedule. In the long-run, all inputs are variable.

While that approach has proven quite valuable, Alchian puts forward a different idea. Instead of assuming which inputs can vary, Alchian argues any producer will choose which input to vary, according to the economic costs. Moreover, the producer chooses the time, T, over which to produce some quantity of goods.

The benefit of Alchian’s framing is that it makes clear there is are not two relevant costs (short-run vs. long-run) to consider for any output. There is just one, the cheapest cost. We can then ask, how do costs (average/marginal/total) vary as T increases? Costs may be decreasing with the time of production, just as we assume costs are lower in the long-run in Viner’s formulation. But that’s a proposition about the derivative of the cost function, not a comparison of two cost functions.

Alchian argues that his more general formulation captures all of the empirical implications of the short-run vs. long-run story. I’ll need to think more about whether that is true.

There is a growing interest in ditching the short-run vs. long-run distinction, independent of Alchian’s work. For example, lots of recent work includes an “adjustment cost” term, acknowledging that all inputs are chosen but that the time frame matters. It seems to be a more tractable approach, more general than fixed vs. freely variable, but without the full generality of Alchian’s approach.

Alchian’s three insights about cost curves complicate the story, even if we ignore all the thorny issues with that cost should be defined as “opportunity cost” and all costs being subjective. Even in the simplest case with an objective cost, there are lots of subtleties to tease through. Thankfully, we can stand on the shoulders of giants like Alchian to make that happen.